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Question 169323This question is from textbook Introductory Algebra
: Solve the problem. A machine can fill 3864 cartons of milk in 0.4 hour. How many cartons of milk can it fill per hour?
This question is from textbook Introductory Algebra
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! the answer is 3864/.4 = 9660
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you answer the question.
x * .4 = 1
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this means what do you need to multiply .4 by in order to make it equal to 1.
you divide both sides of the equation by .4 to get
x = 1/.4 = 2.5
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this means you have to multiply .4 by 2.5 in order to make it equal to 1.
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if you can make 3864 cartons in .4 hours, then you can make 2.5 times that much in 1 hour which equals 9660.
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another way of looking at it is:
you make 3864 in .4 hours.
this translates to 60*.4 = 24 minutes.
if you can make 3864 in 24 minutes, then you can make 3864/24 in 1 minute since 1 minute is 1/24 times 24 minutes.
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3864/24 = 161 cartons per minute.
multiply that by 60 and you get 9660 cartons in 60 minutes.
since 60 minutes equals 1 hour, you get 9660 cartons in 1 hour.
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the basic formula is that the rate per unit time is the number of units produced divided by the time it takes to produce them.
that means 3864/.4 = 9660 units per hour, since the .4 was in hours.
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what you are really doing is dividing 3864 by 1 and then multiplying that by 1 divided by .4 which is the equation for determining how many times you have to multiply .4 hours to get 1 hour.
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long winded answer but i was playing with how to derive number of units per hour from number of units per time other than 1 hour.
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it's a simple process of dividing the number of units by the amount of time it takes to make them.
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alternate example:
3864 units in 4 hours.
how many per hour?
it's 3864 / 4 = 966.
how come?
what do you have to multiply 4 hours to get 1 hour?
equation is:
x * 4 = 1
x = 1/4 = .25
answer is .25
if you can make 3864 in 4 hours, then you can make .25 times as much in 1 hour = 966.
same idea.
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